Forces: Moving Charges in Magnetic Fields

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Video Clips

Lorentz Force (8.02, Spring 2002)

Video RealVideo®
5:26 minutes (13:08 - 18:34)

Worked example finding the radius, period, and frequency of the circular motion of an electron in a uniform magnetic field.

Prior Knowledge: Moving Charges in Uniform Fields (1:21 of video lecture 13)
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Video RealVideo®
5:12 minutes (18:34 - 23:46)

Showing the circular motion of electrons in the magnetic field of a Helmholtz coil using a gas-filled glass tube.

Prior Knowledge: Moving Charges in Uniform Fields (1:21 of video lecture 13)
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Strength of Magnetic Fields (8.02, Spring 2002)

Video RealVideo®
4:05 minutes (17:20 - 21:25)

Definition, including the Lorentz force on a charge moving in a magnetic field. Definition of Tesla and Gauss units for the strength of a magnetic field.

Prior Knowledge: None
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Video RealVideo®
3:30 minutes (21:25 - 24:55)

Explanation of how electrons are used to make image in a TV screen, with a demonstration showing that a magnet will distort this picture when placed near the screen.

Prior Knowledge: Strength of Magnetic Fields (17:20 of video lecture 11)
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Video RealVideo®
6:45 minutes (24:55 - 31:40)

Finding the force on a moving charge in an electric and magnetic field. Finding the total force on a wire in a magnetic field.

Prior Knowledge: Strength of Magnetic Fields (17:20 of video lecture 11)
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Video RealVideo®
6:23 minutes (1:21 - 7:44)

Circular motion of moving particles in constant magnetic fields. Finding the radius of the circular path, with an example for an electron moving in a 1T magnetic field.

Prior Knowledge: Lorentz Force (17:20 of video lecture 11)
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Video RealVideo®
2:28 minutes (12:29 - 14:57)

Using an electron gun and a magnet to show that the path of an electron will curve in the presence of a magnetic field.

Prior Knowledge: Moving Charge in Uniform Magnetic Field (1:21 of video lecture 13)
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Mass Spectrometer (8.02, Spring 2002)

Video RealVideo®
5:33 minutes (14:57 - 20:30)

Definition, with examples of use in separating uranium isotopes for the atomic bomb and for separating isotopes for medical radiation treatments.

Prior Knowledge: Moving Charge in Uniform Magnetic Field (1:21 of video lecture 13)
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Cyclotron (8.02, Spring 2002)

Video RealVideo®
9:10 minutes (20:30 - 29:40)

Definition, with explanation of how a cyclotron is used to accelerate particles with an electric field while containing the particles with a magnetic field. Mention of the use of rings as modern particle accelerators.

Prior Knowledge: Moving Charge in Uniform Magnetic Field (1:21 of video lecture 13)
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Particle Accelerators (8.02, Spring 2002)

Video RealVideo®
5:02 minutes (29:40 - 34:42)

Pictures and discussion of an early cyclotron as well as two modern examples of particle accelerators: Fermilab and CERN.

Prior Knowledge: Cyclotron (20:30 of video lecture 13)
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Video RealVideo®
9:50 minutes (34:42 - 44:32)

Definition, with images of their use in making visible the tracks of electrons and other charged particles. Discussion of the discovery of positrons and other new particles.

Prior Knowledge: Cyclotron (20:30 of video lecture 13)
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Demonstration: Cloud Chamber (8.02, Spring 2002)

Video RealVideo®
4:25 minutes (44:32 - 48:57)

Tracking the motion of electrons and alpha particles in a cloud chamber.

Prior Knowledge: Cloud Chambers (34:42 of video lecture 13)
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Lecture Notes

Magnetic Fields (8.02T, Spring 2005)

Document PDF
Page 1 to page 16

Introduction to magnetism with example of bar magnet. Magnetic field of a bar magnet with diagram; Bar magnets are dipoles. Magnetic monopoles do not exist in isolation. Magnetic Gauss's Law that magnetic flux through a closed surface is zero. Earth's magnetic field, with diagrams and link to a visualization of a bar magnet and Earth's magnetic field

Prior Knowledge: None
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Magnetic Force on Moving Charges (8.02T, Spring 2005)

Document PDF
Page 17 to page 31

Moving charges in a magnetic field feel force perpendicular to both velocity v of charge and direction of magnetic field B. Cross products and the right hand rule, with diagrams and link to a visualization. Lorentz Force F = q(E + v x B), with example of a velocity selector.

Prior Knowledge: Magnetic Fields (pages 1-16 of presentation 14)
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Field Pressures and Tensions (8.02T, Spring 2005)

Document PDF
Page 30 to page 33

Using pressure and tension from E and B fields to understand forces felt by charges. Includes links to visualizations.

Prior Knowledge: Magnetic Fields and Forces (pages 1-31 of presentation 14)
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Magnetic Dipoles: Torque and Force (8.02T, Spring 2005)

Document PDF
Page 5 to page 26

Force and torque on a rectangular current loop in a uniform magnetic field. Magnetic dipole moment μ is defined, with links to visualizations of how torque tends to align μ with B. Force on a magnetic dipole in a non-uniform field, with diagrams. Links to visualizations showing the force on one dipole from another dipole.

Prior Knowledge: Magnetic Fields and Forces (pages 1-31 of presentation 14)
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Document PDF#
Page 14 to page 18

Electric potential; Lorentz force and magnetic force; Biot-Savart Law; Magnetic dipole moments

Prior Knowledge: Material is from Presentations 1-5 and 14-20
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Review: Circuits (8.02T, Spring 2005)

Document PDF#
Page 24 to page 26

Table of important values and equations for resistors, capacitors, and inductors. Brief review of what happens in RC, RL, LC, and RLC circuits.

Prior Knowledge: Material is from Presentations 10, 12, 24, and 25
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Magnetic Fields (8.02T, Spring 2005)

Document PDF
Page 1 to page 2

Magnetic dipoles and their fields are defined, as well as the Lorentz force on a moving charge in a magnetic field.

Prior Knowledge: None
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Magnetic Dipoles (8.02T, Spring 2005)

Document PDF
Page 1 to page 2

Definition of the magnetic dipole moment, with diagrams and equations for force and torque on a magnetic dipole.

Prior Knowledge: Magnetic Fields (R14 and R15)
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Magnetic Forces and Fields (8.022, Fall 2004)

Document PDF
Page 1 to page 6

Magnetism from empirical evidence; Lorentz force on charges and wires; electron trajectories; applications to modern physics; work done by B-fields.

Prior Knowledge: Electric fields
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Online Textbook Chapters

Magnetic Forces (8.02T, Spring 2005)

Document PDF
Page 2 to page 7

B-fields defined; force on moving charge, straight wire; F = 0 for current loop.

Prior Knowledge: Current
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Motion of a Charge (8.02T, Spring 2005)

Document PDF
Page 13 to page 17

Circular and helical motion of charges in B-field; velocity selector and mass spectrometry.

Prior Knowledge: Magnetic forces
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Worked Magnetic Force Problems (8.02T, Spring 2005)

Document PDF
Page 19 to page 23

Using vector product; worked problems on rolling and suspended conducting rods, moving charges, and bar magnet.

Prior Knowledge: Motion of a charge
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Practice Problems

Practicing Right Hand Rules (8.02T, Spring 2005)

Document PDF
Problem 1 to problem 3

Three questions about forces on moving charges in magnetic fields, with answers and explanations.

Prior Knowledge: None
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Hall Effect (8.02T, Spring 2005)

Document PDF
Problem 4

Question about the sign of charge carriers in a slab in a magnetic field, with answer and explanation.

Prior Knowledge: None
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Document PDF
Problem 8

Question about force on one moving charge from another, with answer and explanation.

Prior Knowledge: None
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Free Dipoles (8.02T, Spring 2005)

Document PDF
Problem 5

Question about the attraction between free dipoles, with answer and explanation.

Prior Knowledge: None
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Dipole in Helmholtz Coil (8.02T, Spring 2005)

Document PDF - 1.3 MB
Problem 19 to problem 20

Question about force and torque on a magnetic dipole in a Helmholtz Coil, with answer and explanation.

Prior Knowledge: None
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Parallel Fields (8.02X, Spring 2005)

Document PDF
Problem 1

Describing motion of a particle in parallel E and B fields.

Prior Knowledge: None
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Resting Electron (8.02X, Spring 2005)

Document PDF
Problem 2

Can a resting electron be set in motion with a constant B-field?

Prior Knowledge: None
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Motion of an Ion (8.02X, Spring 2005)

Document PDF
Problem 3

Describing trajectory of an ion through E-field, then B-field.

Prior Knowledge: None
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Nuclei in the LHC (8.02X, Spring 2005)

Document PDF
Problem 3

Finding momentum of nucleus in the Large Hadron Collider and corresponding B-field or E-field.

Prior Knowledge: None
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Exam Questions

Radius of Charged Particle Path (8.02, Spring 2002)

Document PDF
Problem 3

Determining the mass of a particle given its radius of motion in a magnetic field.

Prior Knowledge: None
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Document PDF
Problem 9

Force on electron; balancing electric and magnetic forces.

Prior Knowledge: None
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Document PDF
Problem 2

4-part problem; finding E-field, trajectories for particle; computing kinetic energy. Solution not included.

Prior Knowledge: None
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Magnetic Field Trajectories (8.02X, Spring 2005)

Document PDF
Problem 1

Finding relative charges given trajectories for three particles.

Prior Knowledge: None
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Java Applets

The Magnetosphere of the Earth (8.02T, Spring 2005)

Java Applet Java Applet
Requires Java Virtual Machine

Video animation showing the magnetic field of the earth as well as the magnetic field of the solar wind, which carries the magnetic field of the sun out to the neighborhood of the earth.

Prior Knowledge: None
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Magnetic Merging (8.02T, Spring 2005)

Java Applet Java Applet
Requires Java Virtual Machine

Video animation demonstrating the process of magnetic merging, which is the cause of solar flares.

Prior Knowledge: None
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Java Applet Java Applet
Requires Java Virtual Machine

Applet showing the interaction between the magnetic field lines of the earth and a bar magnet in a classroom at MIT.

Prior Knowledge: None
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Java Applet Java Applet
Requires Java Virtual Machine

Video animation of the magnetic field created by a moving positive charge.

Prior Knowledge: None
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Java Applet Java Applet
Requires Java Virtual Machine

Video animation of the magnetic field created by a moving negative charge.

Prior Knowledge: None
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Java Applet Java Applet
Requires Java Virtual Machine

Video animation showing the magnetic field created by a charge moving in a circular path.

Prior Knowledge: None
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Java Applet Java Applet
Requires Java Virtual Machine

Video animation showing the magnetic field generated by two charges moving in a circular path.

Prior Knowledge: None
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Java Applet Java Applet
Requires Java Virtual Machine

Video animation showing the magnetic field generated by four charges moving in a circular path.

Prior Knowledge: None
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Java Applet Java Applet
Requires Java Virtual Machine

Video animation showing the magnetic field generated by eight charges moving in a circular path.

Prior Knowledge: None
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Java Applet Java Applet
Requires Java Virtual Machine

Video animation showing the magnetic field and force on a charge moving out of the page in a magnetic field that is uniform but changing in strength.

Prior Knowledge: None
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Java Applet Java Applet
Requires Java Virtual Machine

Video animation showing the motion of a charge moving through a uniform upward magnetic field.

Prior Knowledge: None
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Java Applet Java Applet
Requires Java Virtual Machine

Video animation showing a back view of the motion of a charge moving through a uniform upward magnetic field.

Prior Knowledge: None
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The TeachSpin™ Apparatus (8.02T, Spring 2005)

Java Applet Java Applet
Requires Java Virtual Machine

Video animation showing the magnetic field and behavior of a magnet suspended by a spring above a current-carrying wire loop.

Prior Knowledge: None
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The Dip Needle (8.02T, Spring 2005)

Java Applet Java Applet
Requires Java Virtual Machine

Video showing a magnetic dipole moving to align with the magnetic field of the Earth, at a latitude similar to that of Boston.

Prior Knowledge: None
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Java Applet Java Applet
Requires Java Virtual Machine

Video animation showing a giant magnetic dipole moving to align with Earth's magnetic field.

Prior Knowledge: None
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Java Applet Java Applet
Requires Java Virtual Machine

Video animation showing a closer view of a giant magnetic dipole moving to align with Earth's magnetic field.

Prior Knowledge: None
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Java Applet Java Applet
Requires Java Virtual Machine

Video animation showing the magnetic field and motion of a magnet between two coils with sinusoidal and out of phase current.

Prior Knowledge: None
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Magnet Suspended Between Two Coils (8.02T, Spring 2005)

Java Applet Java Applet
Requires Java Virtual Machine

Video animation showing the magnetic field of a magnet suspended between two coils with currents that are sinusoidal and in phase.

Prior Knowledge: None
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Java Applet Java Applet
Requires Java Virtual Machine

Video animations showing the force felt by a charge moving into and then out of a uniform magnetic field.

Prior Knowledge: None
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Java Applet Java Applet
Requires Java Virtual Machine

Applet simulating the magnetic field of a magnetic dipole which is rotating in a uniform magnetic field.

Prior Knowledge: None
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The TeachSpin™ Applet (8.02T, Spring 2005)

Java Applet Java Applet
Requires Java Virtual Machine

Interactive applet simulating the behavior of a magnet attached to a spring between two coils with varying currents.

Prior Knowledge: None
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MIT courses referenced in this section: